Solve for $x$ : $ 4|x + 7| + 2 = 5|x + 7| + 7 $
Answer: Subtract $ {4|x + 7|} $ from both sides: $ \begin{eqnarray} 4|x + 7| + 2 &=& 5|x + 7| + 7 \\ \\ {- 4|x + 7|} && {- 4|x + 7|} \\ \\ 2 &=& 1|x + 7| + 7 \end{eqnarray} $ Subtract $7$ from both sides: $ \begin{eqnarray} 2 &=& 1|x + 7| + 7 \\ \\ {- 7} && {- 7} \\ \\ -5 &=& 1|x + 7| \end{eqnarray} $ Simplify: $ -5 = |x + 7| $ The absolute value cannot be negative. Therefore, there is no solution.